Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions

TL;DR

This work analyzes pure quadratic BHT massive gravity in three dimensions, showing that asymptotically locally flat black holes can be deformed into non-spherical 'black flowers' and extended to dynamical, Robinson-Trautman-like spacetimes that radiate and settle to flowers. By introducing relaxed null-infinity fall-off conditions, the authors retain the BMS$_3$ asymptotic symmetry without central extensions and construct covariant surface charges to obtain conserved quantities, including a finite mass for static and rotating configurations. They find exact expressions for the charges and demonstrate a consistent thermodynamic framework: static black flowers have entropy $S=\frac{\pi b}{4G}$ and obey a first law with $F=M-TS$, while dynamical flowers preserve mass at null infinity and feature gravitational hair through the functions $A(\phi)$ and $\mu$. The results highlight nontrivial horizon structure and hair in a higher-derivative 3D gravity, with explicit connections between asymptotic symmetries, conserved charges, and thermodynamics.

Abstract

The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.